| Issue |
ESAIM: PS
Volume 29, 2025
|
|
|---|---|---|
| Page(s) | 472 - 493 | |
| DOI | https://doi.org/10.1051/ps/2025014 | |
| Published online | 23 December 2025 | |
A pursuit problem for squared Bessel processes
Université Paris-Saclay, CNRS, Univ Evry, Laboratoire de Mathématiques et Modélisation d’Evry,
91037
Evry-Courcouronnes,
France
* Corresponding author: christophe.profeta@univ-evry.fr
Received:
18
November
2024
Accepted:
4
August
2025
In this note, we are interested in the probability that two independent squared Bessel processes do not cross for a long time. We show that this probability has a power decay which is given by the first zero of some hypergeometric function. We also compute along the way the distribution of the location where the crossing eventually occurs.
Mathematics Subject Classification: 60J60 / 60G40 / 60G18
Key words: Bessel process / persistence probability / first passage time
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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